MIGUEL SANCHEZ-PORTAL AND ANA PÉREZ-GARCÍA
Spectroscopy is the main tool for studying the physics of astrophysical objects. Spec-troscopic observations can be thought to be a method by which one samples the emitted spectral energy distribution (SED) from an astronomical source in wavelength bins of size AA. For example, narrow-band-filter photometry is a very-low-resolution spectroscopy technique. The required spectral resolution, i.e. the ability to separate the different spectral features (lines) in the source's SED, is driven by the scientific objectives. The basic parameter for characterizing a given spectrograph configuration is the resolving power. It is defined as R = A/AA, where A A is the difference in wavelength between two closely spaced spectral features, say two spectral lines of equal intensity, each with approximate wavelength A.
There are various spectroscopic techniques, classified according to diverse criteria. We can distinguish three main groups.
• Considering the method of gathering the SED information, we have non-dispersive spectroscopy, such as that performed with X-ray charge-coupled devices (CCDs), whereby the detector is capable of providing information on the energy of the incoming photon; and dispersive spectroscopy, in which the instrument has a dispersive element such as a grating, prism, grism or echelle. In this class, we can include also Fabry-Perot interferometry, tunable filters and Fourier-transform spectrographs.
• According to the "source selection" within the field of view (FoV) we have long-slit spectroscopy, slit-less spectroscopy, slit multi-object spectroscopy (MOS) and three-dimensional spectroscopy. Long-slit spectroscopy is oriented to a single source, point-like or extended, object. Slit-less spectroscopy consists in an objective prism or a simple grism in imaging cameras (for instance XMM/OM). A mask containing "slitlets" placed in the focal plane defines slit MOS (OSIRIS, GMOS, DEIMOS). Three-dimensional spectroscopy allows us to collect simultaneously the spectral and spatial information of an extended object. On the one hand we have the integral field units (IFUs) that use fiber bundles or image slicers, on the other the Fabry-Perot spectrographs and tunable filters.
• According to the spectral resolution: if R < 1000, the spectrograph is said to be of low resolution. If R is higher than 1000 but lower than 5000, the spectrograph is of medium resolution. For R > 10 000, it is said to be of high resolution.
Figure 9.1 shows a typical spectrograph with the common components identified: an entrance slit, a disperser element (grisms, prisms), and a CCD detector. The entrance slit focuses the incoming light; it is used both to set the spectral resolution and to eliminate unnecessary background light. Spectrographs have also an internal lamp for the production of the flat-field and various-wavelength calibration emission-line sources. Both types of calibration lamps are included in the spectrograph in such a way that their light paths through the slit and onto the CCD detector match as closely as possible that
The Emission-Line Universe, ed. J. Cepa. Published by Cambridge University Press. © Cambridge University Press 2009.
of the incoming telescope beam from an astronomical object. Some type of grating (or prism) is needed as a dispersive element.
Grating spectrographs usually cover 1000-2000 A of the optical spectrum at a time with a typical resolution of 0.1-10 A per pixel. To cover a larger spectral range, there are double spectrographs, consisting of two separate spectrographs, which share the incoming light that is divided by a dichroic prism into red and blue beams.
Two common measurements from an astronomical spectrum are those of the flux level as a function of wavelength and of the shape and strength of spectral lines. Absolute-flux observations should be made using a wide slit as the entrance aperture to the spectro-graph, in order to assure that 100% of the source light is collected and to avoid problems related to telescope tracking, seeing changes, and differential refraction. Relative-flux measurements should be determinable to even better levels and the shape of a spectral line would be completely set by the instrumental profile of the spectrograph. Spectroscopy aiming to obtain relative fluxes generally makes use of a narrow slit in order to preserve the best possible spectral resolution. Calibration of the observed-object spectra is normally performed by obtaining spectra of flux-standard stars with the same instrumental setup, including the slit width. During the reduction process, these standard stars are used to assign relative fluxes to the object's spectrum counts as a function of wavelength.
Three factors unrelated to the CCD detector itself are important in the final spectrum result: tracking and guiding errors, seeing changes, and the spectrograph's slit angle. Observations of an astronomical object are obtained, in general, such that the slit matches the object-seeing disk. That is, the slit width is set wide enough to allow most of the point-spread function (PSF) (for a point source) to pass through but kept small enough to prevent as much of the sky background as possible from entering the spectrograph. Therefore, changes in the guiding or image seeing will cause more or less source light to enter through the slit. These effects cannot be corrected in our final image. Finally, when we observe an object, for a given distance to the zenith, a different image for each wavelength is formed in the telescope's focal plane. Also, for a selected wavelength, the location of the image in the focal plane depends on the distance from the zenith. These effects are caused by differential atmospheric diffraction (Filippenko 1982). All objects in the sky become slightly prismatic due to this differential atmospheric diffraction. If the spectrograph's slit is not placed parallel to the direction of atmospheric dispersion, light loss that is not chromatically uniform may occur in the slit. Atmospheric dispersion is caused by the variation of the angle of refraction of a light ray as a function of its wavelength, and the direction parallel to this dispersion is called the parallactic angle. Aligning the slit at the parallactic angle solves this problem. The parallactic angle can be determined as cos(object declination) x sin(parallactic angle) = sign(hour angle) x cos(observer's latitude) x sin(object azimuth).
To get an idea of how important this can be, just take into account that even at a modest sec(z) = 1.5, an image at 4000 A is displaced towards the zenith by 1.1 arcsec relative to the image at 6000 A. If we are trying to observe over this wavelength range using a 2-arcsec slit, we will suffer a large amount of light loss unless the slit is placed at the parallactic angle.
9.2.1 Signal-to-noise calculations The equation for the signal-to-noise ratio (SNR) of a measurement made with a CCD is given by
where N* is the total number of photons collected from the object of interest (signal). The noise term includes the square roots of N*, plus npix (the number of pixels under consideration) times the contributions from NS (the total number of photons per pixel from the sky), ND (the total number of dark-current electrons per pixel, which in all CCDs is now negligible), and NR (the total number of electrons per pixel resulting from the reading noise). For bright sources, S/N <x Vn , whereas for faint sources we must use the entire expression. For spectroscopic observations the largest noise contributors that will degrade the resulting signal-to-noise ratio are the background sky and how well the data have been flat-fielded.
In spectroscopy, it is possible to calculate the SNR for the continuum and for a given spectral line. In the continuum case, the number of pixels used in the SNR calculations can be determined by multiplying the continuum bandpass range over which the SNR
is desired by the finite width of the spectrum on the CCD. For example, a spectrograph might have an image scale of 0.7 A per pixel and the imaged spectrum a width of five pixels on the array in the direction perpendicular to the dispersion. To calculate the SNR for the spectral continuum over a 200-A bandpass, one would use npix = 1428. In contrast, a narrow line with a full width at zero intensity of 40 A would use npix = 286. The SNR of the emission line would therefore be higher due to the smaller overall error contribution, and also because the emission-line flux is higher. Signal-to-noise calculations are useful in predicting observational values, such as the integration time.
9.3. Effects to correct in a long-slit spectrum
The bias level of a CCD camera consists of an added current intended to avoid negative values in the reading of the CCD. This zero level is independent of the integration duration of an exposure and should be theoretically constant for all pixels. In reality, there may some (very-low-level) variations in structure. To correct for this effect, every observing night a sufficiently large number of bias images, i.e. zero-length exposures with the shutter closed, is taken. Figure 9.2 shows an example of a bias frame.
Also, preceding read-out and after read-out of all pixels of the CCD, the read-out electronics will perform several additional cycles that do not correspond to physical pixels. These virtual pixels are referred to as overscan, and will be written as part of the CCD image. The overscan will be used to subtract the mean value of the zero level.
9.3.2 Flat-field and illumination corrections Each pixel within the CCD array has its own unique light-sensitivity characteristics. Since these characteristics affect camera performance, they must be removed through calibration. The calibration image to correct this effect is the flat-field frame, that measures the response of each pixel in the CCD array to illumination and is used to correct for any variation in illumination over the field of the array (Figure 9.3). In spectroscopy, typically we use a quartz lamp or dome screen. This flat-field image requires a high SNR.
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